CHAPTER 10 D.C. POWER

10.1     POWER UNITS

Power is defined as the rate of using (or providing) energy and, in the electrical world, is measured in the unit ‘watt’ (W).

In the mechanical world of hydraulics, power is the product of pressure and volume flow.  In modern SI units pressure is measured in newtons per square metre (N/m²) and volume flow in cubic metres per second.  The product of these two

N	x	m3	=	Nm	=	J	=	W
m2		s		s		s

The electrical equivalent of pressure is the volt, and the electrical equivalent of hydraulic flow is the ampere, so that the power in watts is the product of voltage and current - that is

W = V x I

where V is measured in volts and / in amperes; W is then in watts.

Applying Ohm’s Law

V

=

IR

or

I

=

V

to this formula:

R

W

=

IR

x

I

=

I2R

or

W

=

V

x

V

=

V2

R

R

These are two alternative forms for power when only I and R, or when only V and R, are known.

In earlier years the power output of electric motors was measured in ‘horsepower’ to align them with mechanical engine practice.  Many motor nameplates are still marked in ‘hp’, but more and more are now being marked in kilowatts (kW).

The kilowatt used in this case is the equivalent of the mechanical power output of the motor. Horsepower and kilowatts are directly related:

                                                         

The horsepower in this case is British horsepower.  (Some Continental countries use a slightly different unit, known as the ‘metric horsepower’, which is equivalent to 0.735kW, a difference of about 1½%.)

Special care is needed when referring to the power of motors.  Motors are rated by their mechanical output (hp or kW), but, because no motor is 100% efficient, its electrical power input, also measured in kW, is always greater than its mechanical power output.  Because both may be measured in kilowatts, confusion can easily arise.  When it is desired to distinguish between mechanical output and electrical input, suffixes ‘m’ and ‘e’ are often used: thus output is kW_m and input kW_e. Their ratio is the efficiency of the motor, thus:

kWm	=	efficiency
kWe

Power - that is, the rate of producing, absorbing or transmitting energy - is in the SI system always measured in watts or, more usually, kilowatts.  It occurs in fields other than electricity and mechanics.  For example energy can be produced thermally in boilers or reactors, or chemically in batteries or by burning fuel.  The power being developed is still measured in kilowatts and would be distinguished by suffixes ‘kW_th’ or ‘kW_ch’.